Details

sample117.0ms

Algorithm

intervals

Results

56.0ms	122×	body	1280	valid
18.0ms	256×	pre	80	true
13.0ms	54×	body	640	valid
4.0ms	23×	body	320	valid
2.0ms	48×	body	80	valid
1.0ms	9×	body	160	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	33	5
3	39	5
4	50	5
5	70	5
6	99	5
7	124	5
8	166	5
9	259	5
10	260	5
11	260	5

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 13.4b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.2b	(- (tan (+ y z)) (tan a))
4.6b	(tan (+ y z))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`associate-+r+`
10×	`add-log-exp`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `fma-def` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `tan-sum` `diff-log` `sum-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

3 → 72

Calls

3 calls:

7.0ms	(+ x (- (tan (+ y z)) (tan a)))
12.0ms	(- (tan (+ y z)) (tan a))
5.0ms	(tan (+ y z))

series319.0ms

Counts

3 → 9

Calls

3 calls:

137.0ms	(+ x (- (tan (+ y z)) (tan a)))
128.0ms	(- (tan (+ y z)) (tan a))
55.0ms	(tan (+ y z))

simplify100.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	276	685
1	732	540
2	3128	507
3	5001	488

prune242.0ms

Filtered

81 candidates to 59 candidates (72.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	71	10	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	10	82

Merged error: 0.1b

Counts

82 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.1b	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.2b	(* (tan y) (tan z))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

165×	`*-un-lft-identity`
115×	`add-sqr-sqrt`
108×	`add-cube-cbrt` `prod-diff`
97×	`times-frac`
56×	`associate-+r+`
27×	`distribute-lft-out`
18×	`fma-neg`
16×	`associate-/r/`
11×	`add-log-exp`
9×	`flip3--` `flip--`
8×	`add-exp-log` `add-cbrt-cube` `div-inv`
7×	`tan-quot`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*`
3×	`fma-def` `associate-r` `associate-l` `associate-/r*` `associate-/l/`
2×	`sub-neg` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `+-commutative` `frac-times` `associate-+r-` `frac-2neg` `associate-r/` `div-exp` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `clear-num` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 227

Calls

4 calls:

19.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
9.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
15.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
9.0ms	(* (tan y) (tan z))

series1.1s

Counts

4 → 12

Calls

4 calls:

370.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
238.0ms	(/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z))))
420.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
105.0ms	(* (tan y) (tan z))

simplify92.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	704	4490
1	2293	3769
2	5002	3667

prune679.0ms

Filtered

239 candidates to 145 candidates (60.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	230	9	239
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	235	14	249

Merged error: 0.1b

Counts

249 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (tan y) (tan z))
0.2b	(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (tan a)))
0.2b	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
40×	`tan-quot`
20×	`add-exp-log` `add-cbrt-cube`
19×	`frac-times` `pow-prod-down`
13×	`associate-r/` `associate-l/`
12×	`add-sqr-sqrt`
10×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`pow-plus` `unswap-sqr`
1×	`pow2` `swap-sqr` `fma-udef`

Counts

4 → 107

Calls

4 calls:

6.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))
1.0ms	(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (tan a)))
11.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

series1.1s

Counts

4 → 12

Calls

4 calls:

100.0ms	(* (tan y) (tan z))
101.0ms	(* (tan y) (tan z))
808.0ms	(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (* (* (tan y) (tan z)) (* (tan y) (tan z))))) (+ 1 (* (tan y) (tan z))) (- (tan a)))
129.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))

simplify63.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	422	1108
1	1870	953
2	5002	930

prune412.0ms

Filtered

119 candidates to 75 candidates (63.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	121	12	133

Merged error: 0.0b

Counts

133 → 12

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan y) (tan z))
0.2b	(* (sin y) (sin z))
0.2b	(* (* (tan y) (tan z)) (* (sin y) (sin z)))
0.2b	(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (/ (* (* (tan y) (tan z)) (* (sin y) (sin z))) (* (cos y) (cos z))))) (+ 1 (* (tan y) (tan z))) (- (tan a)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`tan-quot` `add-sqr-sqrt`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r` `associate-l`
6×	`frac-times` `associate-*l/`
5×	`sin-mult`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`fma-udef`

Counts

4 → 85

Calls

4 calls:

5.0ms	(* (tan y) (tan z))
5.0ms	(* (sin y) (sin z))
10.0ms	(* (* (tan y) (tan z)) (* (sin y) (sin z)))
1.0ms	(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (/ (* (* (tan y) (tan z)) (* (sin y) (sin z))) (* (cos y) (cos z))))) (+ 1 (* (tan y) (tan z))) (- (tan a)))

series1.2s

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (tan y) (tan z))
49.0ms	(* (sin y) (sin z))
184.0ms	(* (* (tan y) (tan z)) (* (sin y) (sin z)))
855.0ms	(fma (/ (+ (tan y) (tan z)) (- (* 1 1) (/ (* (* (tan y) (tan z)) (* (sin y) (sin z))) (* (cos y) (cos z))))) (+ 1 (* (tan y) (tan z))) (- (tan a)))

simplify77.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	465	1056
1	2231	912
2	5001	911

prune435.0ms

Filtered

97 candidates to 69 candidates (71.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	97	12	109

Merged error: 0.0b

Counts

109 → 12

regimes681.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	24
1	34	24

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	3888×	body	1280	valid
542.0ms	8000×	pre	80	true
484.0ms	1964×	body	640	valid
129.0ms	743×	body	320	valid
62.0ms	1152×	body	80	valid
32.0ms	253×	body	160	valid